Attention deficits linked with proclivity to explore while foraging.

All mobile organisms forage for resources, choosing how and when to search for new opportunities by comparing current returns with the average for the environment. In humans, nomadic lifestyles favouring exploration have been associated with genetic mutations implicated in attention deficit hyperactivity disorder (ADHD), inviting the hypothesis that this condition may impact foraging decisions in the general population. Here we tested this pre-registered hypothesis by examining how human participants collected resources in an online foraging task. On every trial, participants chose either to continue to collect rewards from a depleting patch of resources or to replenish the patch. Participants also completed a well-validated ADHD self-report screening assessment at the end of sessions. Participants departed resource patches sooner when travel times between patches were shorter than when they were longer, as predicted by optimal foraging theory. Participants whose scores on the ADHD scale crossed the threshold for a positive screen departed patches significantly sooner than participants who did not meet this criterion. Participants meeting this threshold for ADHD also achieved higher reward rates than individuals who did not. Our findings suggest that ADHD attributes may confer foraging advantages in some environments and invite the possibility that this condition may reflect an adaptation favouring exploration over exploitation.

Relative numerical middle in rhesus monkeys.

Animals show vast numerical competence in tasks that require both ordinal and cardinal numerical representations, but few studies have addressed whether animals can identify the numerical middle in a sequence. Two rhesus monkeys (Macaca mulatta) learned to select the middle dot in a horizontal sequence of three dots on a touchscreen. When subsequently presented with longer sequences composed of 5, 7 or 9 items, monkeys transferred the middle rule. Accuracy decreased as the length of the sequence increased. In a second test, we presented monkeys with asymmetrical sequences composed of nine items, where the numerical and spatial middle were distinct and both monkeys selected the numerical middle over the spatial middle. Our results demonstrate that rhesus macaques can extract an abstract numerical rule to bisect a discrete set of items.

Context-Dependent Modulation of Early Visual Cortical Responses to Numerical and Nonnumerical Magnitudes.

Whether and how the brain encodes discrete numerical magnitude differently from continuous nonnumerical magnitude is hotly debated. In a previous set of studies, we orthogonally varied numerical (numerosity) and nonnumerical (size and spacing) dimensions of dot arrays and demonstrated a strong modulation of early visual evoked potentials (VEPs) by numerosity and not by nonnumerical dimensions. Although very little is known about the brain's response to systematic changes in continuous dimensions of a dot array, some authors intuit that the visual processing stream must be more sensitive to continuous magnitude information than to numerosity. To address this possibility, we measured VEPs of participants viewing dot arrays that changed exclusively in one nonnumerical magnitude dimension at a time (size or spacing) while holding numerosity constant and compared this to a condition where numerosity was changed while holding size and spacing constant. We found reliable but small neural sensitivity to exclusive changes in size and spacing; however, exclusively changing numerosity elicited a much more robust modulation of the VEPs. Together with previous work, these findings suggest that sensitivity to magnitude dimensions in early visual cortex is context dependent: The brain is moderately sensitive to changes in size and spacing when numerosity is held constant, but sensitivity to these continuous variables diminishes to a negligible level when numerosity is allowed to vary at the same time. Neurophysiological explanations for the encoding and context dependency of numerical and nonnumerical magnitudes are proposed within the framework of neuronal normalization.

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals.

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

Approximate multiplication in young children prior to multiplication instruction.

Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can perform a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruction. We presented 5- to 8-year-olds with nonsymbolic multiplicands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a visible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multiplication, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 × 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between children's Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children's emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.

Similarly oriented objects appear more numerous.

Several non-numerical factors influence the numerical estimation of visual arrays, including the spacing of items and whether they are arranged randomly or symmetrically. Here we report a novel numerosity illusion we term the coherence illusion. When items in an array have a coherent orientation (all pointing in the same direction) they seem to be more numerous than when items are oriented randomly. Participants show parametric effects of orientation coherence in three distinct numerical judgment tasks. These findings are not predicted by any current model of numerical estimation. We discuss array entropy as a possible framework for explaining both the coherence illusion and the previously reported regular-random illusion.

Shared and distinct neural circuitry for nonsymbolic and symbolic double-digit addition.

Symbolic arithmetic is a complex, uniquely human ability that is acquired through direct instruction. In contrast, the capacity to mentally add and subtract nonsymbolic quantities such as dot arrays emerges without instruction and can be seen in human infants and nonhuman animals. One possibility is that the mental manipulation of nonsymbolic arrays provides a critical scaffold for developing symbolic arithmetic abilities. To explore this hypothesis, we examined whether there is a shared neural basis for nonsymbolic and symbolic double-digit addition. In parallel, we asked whether there are brain regions that are associated with nonsymbolic and symbolic addition independently. First, relative to visually matched control tasks, we found that both nonsymbolic and symbolic addition elicited greater neural signal in the bilateral intraparietal sulcus (IPS), bilateral inferior temporal gyrus, and the right superior parietal lobule. Subsequent representational similarity analyses revealed that the neural similarity between nonsymbolic and symbolic addition was stronger relative to the similarity between each addition condition and its visually matched control task, but only in the bilateral IPS. These findings suggest that the IPS is involved in arithmetic calculation independent of stimulus format.

Developmental trajectory of neural specialization for letter and number visual processing.

Adult neuroimaging studies have demonstrated dissociable neural activation patterns in the visual cortex in response to letters (Latin alphabet) and numbers (Arabic numerals), which suggest a strong experiential influence of reading and mathematics on the human visual system. Here, developmental trajectories in the event-related potential (ERP) patterns evoked by visual processing of letters, numbers, and false fonts were examined in four different age groups (7-, 10-, 15-year-olds, and young adults). The 15-year-olds and adults showed greater neural sensitivity to letters over numbers in the left visual cortex and the reverse pattern in the right visual cortex, extending previous findings in adults to teenagers. In marked contrast, 7- and 10-year-olds did not show this dissociable neural pattern. Furthermore, the contrast of familiar stimuli (letters or numbers) versus unfamiliar ones (false fonts) showed stark ERP differences between the younger (7- and 10-year-olds) and the older (15-year-olds and adults) participants. These results suggest that both coarse (familiar versus unfamiliar) and fine (letters versus numbers) tuning for letters and numbers continue throughout childhood and early adolescence, demonstrating a profound impact of uniquely human cultural inventions on visual cognition and its development.

Numerosity processing in early visual cortex.

While parietal cortex is thought to be critical for representing numerical magnitudes, we recently reported an event-related potential (ERP) study demonstrating selective neural sensitivity to numerosity over midline occipital sites very early in the time course, suggesting the involvement of early visual cortex in numerosity processing. However, which specific brain area underlies such early activation is not known. Here, we tested whether numerosity-sensitive neural signatures arise specifically from the initial stages of visual cortex, aiming to localize the generator of these signals by taking advantage of the distinctive folding pattern of early occipital cortices around the calcarine sulcus, which predicts an inversion of polarity of ERPs arising from these areas when stimuli are presented in the upper versus lower visual field. Dot arrays, including 8-32dots constructed systematically across various numerical and non-numerical visual attributes, were presented randomly in either the upper or lower visual hemifields. Our results show that neural responses at about 90ms post-stimulus were robustly sensitive to numerosity. Moreover, the peculiar pattern of polarity inversion of numerosity-sensitive activity at this stage suggested its generation primarily in V2 and V3. In contrast, numerosity-sensitive ERP activity at occipito-parietal channels later in the time course (210-230ms) did not show polarity inversion, indicating a subsequent processing stage in the dorsal stream. Overall, these results demonstrate that numerosity processing begins in one of the earliest stages of the cortical visual stream.

Rapid and Direct Encoding of Numerosity in the Visual Stream.

Humans are endowed with an intuitive number sense that allows us to perceive and estimate numerosity without relying on language. It is controversial, however, as to whether there is a neural mechanism for direct perception of numerosity or whether numerosity is perceived indirectly via other perceptual properties. In this study, we used a novel regression-based analytic method, which allowed an assessment of the unique contributions of visual properties, including numerosity, to explain visual evoked potentials of participants passively viewing dot arrays. We found that the human brain is uniquely sensitive to numerosity and more sensitive to changes in numerosity than to changes in other visual properties, starting extremely early in the visual stream: 75 ms over a medial occipital site and 180 ms over bilateral occipitoparietal sites. These findings provide strong evidence for the existence of a neural mechanism for rapidly and directly extracting numerosity information in the human visual pathway.

Five-year-olds do not show ambiguity aversion in a risk and ambiguity task with physical objects.

Ambiguity aversion arises when a decision maker prefers risky gambles with known probabilities over equivalent ambiguous gambles with unknown probabilities. This phenomenon has been consistently observed in adults across a large body of empirical work. Evaluating ambiguity aversion in young children, however, has posed methodological challenges because probabilistic representations appropriate for adults might not be understood by young children. Here, we established a novel method for representing risk and ambiguity with physical objects that overcomes previous methodological limitations and allows us to measure ambiguity aversion in young children. We found that individual 5-year-olds exhibited consistent choice preferences and, as a group, exhibited no ambiguity aversion in a task that evokes ambiguity aversion in adults. Across individuals, 5-year-olds exhibited greater variance in ambiguity preferences compared with adults tested under similar conditions. This suggests that ambiguity aversion is absent during early childhood and emerges over the course of development.

The evolution of self-control.

Cognition presents evolutionary research with one of its greatest challenges. Cognitive evolution has been explained at the proximate level by shifts in absolute and relative brain volume and at the ultimate level by differences in social and dietary complexity. However, no study has integrated the experimental and phylogenetic approach at the scale required to rigorously test these explanations. Instead, previous research has largely relied on various measures of brain size as proxies for cognitive abilities. We experimentally evaluated these major evolutionary explanations by quantitatively comparing the cognitive performance of 567 individuals representing 36 species on two problem-solving tasks measuring self-control. Phylogenetic analysis revealed that absolute brain volume best predicted performance across species and accounted for considerably more variance than brain volume controlling for body mass. This result corroborates recent advances in evolutionary neurobiology and illustrates the cognitive consequences of cortical reorganization through increases in brain volume. Within primates, dietary breadth but not social group size was a strong predictor of species differences in self-control. Our results implicate robust evolutionary relationships between dietary breadth, absolute brain volume, and self-control. These findings provide a significant first step toward quantifying the primate cognitive phenome and explaining the process of cognitive evolution.

Direct and rapid encoding of numerosity in the visual stream.

The target article dismisses all prior work purporting to demonstrate that number is a conceptual primitive. Here, we take issue with their misrepresentation of our recent line of work on numerosity perception, which demonstrates rapid and direct encoding of numerosity and undermines the thesis of the target article that "continuous magnitudes are more automatic and basic than numerosities" (sect. 1, para. 2).

Comparison of discrete ratios by rhesus macaques (Macaca mulatta).

Perceiving and comparing ratios are crucial skills for humans. Little is known about whether other animals can compare ratios. We trained two rhesus macaques (Macaca mulatta) to choose arrays that contained the greater ratio of positive to negative stimuli, regardless of the absolute number of stimuli in each of the two choice arrays. Subjects learned this task, and their performance generalized to novel ratios. Moreover, performance was modulated by the ratio between ratios; subjects responded more quickly and accurately when the ratio between ratios was higher. Control conditions ruled out the possibility that subjects were relying on surface area, although the ratio between ratios of surface area did seem to influence their choices. Our results demonstrate that rhesus monkeys can compare discrete ratios, demonstrating not only proportional reasoning ability but also the ability to reason about relations between relations.

Monkeys display classic signatures of human symbolic arithmetic.

Non-human primates compare quantities in a crude manner, by approximating their values. Less is known about the mental transformations that non-humans can perform over approximate quantities, such as arithmetic transformations. There is evidence that human symbolic arithmetic has a deep psychological connection with the primitive, approximate forms of quantification of non-human animals. Here, we ask whether the subtle performance signatures that humans exhibit during symbolic arithmetic also bear a connection to primitive arithmetic. Specifically, we examined the problem size effect, the tie effect, and the practice effect-effects which are commonly observed in children's math performance in school. We show that, like humans, monkeys exhibited the problem size and tie effects, indicating commonalities in arithmetic algorithms with humans. Unlike humans, however, monkeys did not exhibit a practice effect. Together, these findings provide new evidence for a cognitive relation between non-symbolic and symbolic arithmetic.

Non-symbolic approximate arithmetic training improves math performance in preschoolers.

Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words.

Number sense in infancy predicts mathematical abilities in childhood.

Human infants in the first year of life possess an intuitive sense of number. This preverbal number sense may serve as a developmental building block for the uniquely human capacity for mathematics. In support of this idea, several studies have demonstrated that nonverbal number sense is correlated with mathematical abilities in children and adults. However, there has been no direct evidence that infant numerical abilities are related to mathematical abilities later in childhood. Here, we provide evidence that preverbal number sense in infancy predicts mathematical abilities in preschool-aged children. Numerical preference scores at 6 months of age correlated with both standardized math test scores and nonsymbolic number comparison scores at 3.5 years of age, suggesting that preverbal number sense facilitates the acquisition of numerical symbols and mathematical abilities. This relationship held even after controlling for general intelligence, indicating that preverbal number sense imparts a unique contribution to mathematical ability. These results validate the many prior studies purporting to show number sense in infancy and support the hypothesis that mathematics is built upon an intuitive sense of number that predates language.

Experience-dependent hemispheric specialization of letters and numbers is revealed in early visual processing.

Recent fMRI research has demonstrated that letters and numbers are preferentially processed in distinct regions and hemispheres in the visual cortex. In particular, the left visual cortex preferentially processes letters compared with numbers, whereas the right visual cortex preferentially processes numbers compared with letters. Because letters and numbers are cultural inventions and are otherwise physically arbitrary, such a double dissociation is strong evidence for experiential effects on neural architecture. Here, we use the high temporal resolution of ERPs to investigate the temporal dynamics of the neural dissociation between letters and numbers. We show that the divergence between ERP traces to letters and numbers emerges very early in processing. Letters evoked greater N1 waves (latencies 140-170 msec) than did numbers over left occipital channels, whereas numbers evoked greater N1s than letters over the right, suggesting letters and numbers are preferentially processed in opposite hemispheres early in visual encoding. Moreover, strings of letters, but not single letters, elicited greater P2 ERP waves (starting around 250 msec) than numbers did over the left hemisphere, suggesting that the visual cortex is tuned to selectively process combinations of letters, but not numbers, further along in the visual processing stream. Additionally, the processing of both of these culturally defined stimulus types differentiated from similar but unfamiliar visual stimulus forms (false fonts) even earlier in the processing stream (the P1 at 100 msec). These findings imply major cortical specialization processes within the visual system driven by experience with reading and mathematics.

Electrophysiological evidence for the involvement of the approximate number system in preschoolers' processing of spoken number words.

Little is known about the neural underpinnings of number word comprehension in young children. Here we investigated the neural processing of these words during the crucial developmental window in which children learn their meanings and asked whether such processing relies on the Approximate Number System. ERPs were recorded as 3- to 5-year-old children heard the words one, two, three, or six while looking at pictures of 1, 2, 3, or 6 objects. The auditory number word was incongruent with the number of visual objects on half the trials and congruent on the other half. Children's number word comprehension predicted their ERP incongruency effects. Specifically, children with the least number word knowledge did not show any ERP incongruency effects, whereas those with intermediate and high number word knowledge showed an enhanced, negative polarity incongruency response (N(inc)) over centroparietal sites from 200 to 500 msec after the number word onset. This negativity was followed by an enhanced, positive polarity incongruency effect (P(inc)) that emerged bilaterally over parietal sites at about 700 msec. Moreover, children with the most number word knowledge showed ratio dependence in the P(inc) (larger for greater compared with smaller numerical mismatches), a hallmark of the Approximate Number System. Importantly, a similar modulation of the P(inc) from 700 to 800 msec was found in children with intermediate number word knowledge. These results provide the first neural correlates of spoken number word comprehension in preschoolers and are consistent with the view that children map number words onto approximate number representations before they fully master the verbal count list.

Lemurs and macaques show similar numerical sensitivity.

We investigated the precision of the approximate number system (ANS) in three lemur species (Lemur catta, Eulemur mongoz, and Eulemur macaco flavifrons), one Old World monkey species (Macaca mulatta) and humans (Homo sapiens). In Experiment 1, four individuals of each nonhuman primate species were trained to select the numerically larger of two visual arrays on a touchscreen. We estimated numerical acuity by modeling Weber fractions (w) and found quantitatively equivalent performance among all four nonhuman primate species. In Experiment 2, we tested adult humans in a similar procedure, and they outperformed the four nonhuman species but showed qualitatively similar performance. These results indicate that the ANS is conserved over the primate order.